“led by an invisible hand to promote an end which was no part of his intention.”
An invisible hand of market economies is only the technical logic of arbitrage operating under available capital constraints and moving utility, useful goods and services, from plenty to scarcity, low to high price, on an opportunity cost, seen and unseen, determination of purchase and selling price. People are then led by an invisible hand of price differentials and profit making to perform to the common good without conscious intent.
If there weren't unmet needs in goods or services in the presence of disposable end user opportunity capital, which is that money available to be spent on an opportunity cost basis, there would be no arbitrage profit possible and therefore, the purpose of a market being profit, no market possible.
There are two aspects to price discovery which defines the possibilities of arbitrage in both buying and selling. Value is utility (x) scarcity and end user maximum price is (utility (x) scarcity) ÷ (available end user opportunity capital) which defines all other prices. The arbitrage purchase price has to be lower than the maximum possible end user purchase price or the market fails. That arbitrage purchase price, both estimated and realized, in relation to the maximum possible end user purchase price, defines all possible market transactions.
Arbitrage is done on a basis of risk and reward. Arbitrageurs are taking a chance that their purchase price will be enough lower than their selling price to cover expenses and return a profit. That risk, and that reward when it pays off, guiding behavior, constitute a so-called invisible hand of the market. The only harmony of interests is that both buyer and seller desire a complete transaction at maximum benefit to each of them. It's a negotiation of the possible. Every market transaction is a zero sum game but the cumulative effect, by guiding the allocation of resources to produce for maximum return, is wealth creation. That's the market magic that led Adam Smith into talk of the irrational.
Do Well and Be Well
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